Key points:

He wants to introduce a banking royal commission bill later this month

But Finance Minister says even if it passed through both Houses of Parliament, the Government would not pay for it

The Government's longstanding policy has been against holding a royal commission, but Nationals senator Barry O'Sullivan has confirmed he is considering introducing a backbench bill for a public banking inquiry.

He was emboldened by how quickly the Senate moved to debate Liberal senator Dean Smith's same-sex marriage bill, which had cross-party support.

"My colleague Dean Smith has shown the way," Senator O'Sullivan said.

"I can tell you that there are quite a lot of excited backbenchers — Senate side at least — in the Government ranks, who are now contemplating what they may do with serious issues that they want aired and debated in the Parliament."

Senator O'Sullivan said he could introduce a banking royal commission bill when Parliament resumes later this month, using the same approach.

"What we've seen this week was a private senator's bill able to take precedence in the Senate over government business because it had sufficient support on the floor of the Senate," Senator O'Sullivan said.

"I know that the call for a commission of inquiry [into banks] has the same level of support in the Senate, so if I do introduce a motion I anticipate it would be very successful."

Some conservatives are privately welcoming the push for a banking inquiry, describing it as revenge and retribution.

They are unhappy with the way the Government has handled the same-sex marriage issue and are not satisfied by the compromise offered internally on religious protections.

Coalition says it won't fund inquiry

Finance Minister Mathias Cormann was quick to scotch the proposal, saying even if it passed through both Houses of Parliament the Government would not pay for it.

"Only the Government can make the relevant appropriation to give effect to a royal commission and the Government's position is not to do that," he told Sky News.

The Prime Minister also argued it was not necessary, because the Government had already funded a crackdown on the banking sector and further protections for consumers.

"All of the recommendations that a royal commission would be likely to make are being undertaken now," Prime Minister Malcolm Turnbull said in Sydney.

Senator O'Sullivan said while he was not seeking a postal survey into banking, he thought it too would have emphatic public backing.

"I say to you that if we were to survey the Australian people in relation to their attitudes around banks and financial services and insurance and the like, we'd get a similar result of people who are unhappy with the banks," he said.

Would the inquiry get through Parliament?

Labor and the Greens have long advocated for a banking royal commission to be established, along with many crossbenchers.